OFFSET
1,1
COMMENTS
Erdős (1970) proved that the asymptotic density of this sequence exists and is less than 1.
The numbers of terms not exceeding 10^k for k = 1, 2, ... are 0, 1, 37, 543, 6529, 73578, 798916, 8480417, 88832422, ...
Any positive multiple of any term of this sequence is also a term. The primitive terms are in A336443.
LINKS
Amiram Eldar, Table of n, a(n) for n = 1..10000
Paul Erdős, Some extremal problems in combinatorial number theory, in the book Hari Shankar (ed.), Mathematical Essays Dedicated to A. J. Macintyre, Ohio Univ. Press, Athens, Ohio (1970), pp. 123-133.
EXAMPLE
60 is a term since {3, 4, 5} are divisors of 60, gcd(3,4) = gcd(4,5) = gcd(3,5) = 1 and 3 < 4 < 5 < 2*3.
MATHEMATICA
divQ[n_] := AnyTrue[Subsets[Divisors[n], {3}], And @@ CoprimeQ @@@ Subsets[#, {2}] && #[[3]] < 2 * #[[1]] &]; Select[Range[1500], divQ]
CROSSREFS
KEYWORD
nonn
AUTHOR
Amiram Eldar, Jul 21 2020
STATUS
approved